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Richard Fitzpatrick

Publications and source records attributed to Richard Fitzpatrick.

14 recordsLinked to original sources
arXiv2026

Macroscopic Stability of a Rapidly Rotating Theta Pinch

The macroscopic ideal-MHD stability of an axisymmetric mirror device with sonic levels of plasma rotation is analyzed by approximating the plasma equilibrium as a rotating theta pinch possessing an artificial gravity. An eigenmode equation is derived that governs the stability of the equilibrium to small perturbations in the case of an arbitrary plasma angular velocity profile. The stability of the m=1 and m=2 modes is investigated. The plasma is found to be stable to these two modes provided that it is sufficiently short in the axial direction. The critical axial length of the device below which the modes are stabilized first decreases with increasing plasma rotation, attains a minimum value when the rotation is roughly sonic, and then increases with increasing plasma rotation. The value of the plasma rotation off the magnetic axis is found to have a significantly stronger effect on the stability of the modes than the value on the magnetic axis.

physics.plasm-ph↗
arXiv2026

Equilibrium of a Rapidly Rotating Axisymmetric Magnetic Mirror Machine

A recent paper [Hazeltine, et al., Phys. Plasmas 33, 072501 (2026)] has questioned whether the standard result, (ultimately) due to Ferraro, that the plasma angular velocity is approximately constant along individual equilibrium magnetic field-lines in a rotating axisymmetric magnetic mirror machine, continues to hold when the rotation becomes sonic or supersonic. In order to resolve this issue, the equilibrium of a rapidly rotating mirror is investigated, starting from first principles, using an ideal two-fluid model with anisotropic pressure. It is found that, as long as the ion gyro-radius is much less than the machine size, and the angular velocity of the plasma is much less than the ion gyro-frequency, the Ferraro result holds good.

physics.plasm-ph↗
arXiv2026

A simple model of current ramp down in the ITER tokamak

The controlled ramp down of the toroidal plasma current in the ITER tokamak is simulated using a simple model that employs cylindrical geometry. The magnetohydrodynamical (MHD) stability of the plasma throughout the whole current ramp is also calculated. The only potentially unstable MHD mode is the m=2/n=1 classical tearing mode. The envisioned 60 second ramp down of the plasma current in ITER is found to be perfectly feasible, provided that the plasma is sufficiently hot at the start of the ramp. However, attempts to ramp down the current on a significantly faster time scale are predicted to excite 2/1 tearing modes that are likely to lock to the vacuum vessel, and trigger a disruption.

physics.plasm-ph↗
arXiv2026

Resistive instabilities of current sheets in stratified plasmas with a gravitational field

Magnetic reconnection can develop spontaneously via the tearing instability, often invoked to explain disruptive instabilities in fusion devices, solar flares, the generation of periodic density disturbances at the tip of helmet streamers, and flux transfer events at the Earth's dayside magnetopause. However, in many such environments the presence of gravity, magnetic field curvature or other forms of acceleration often result in situations of a heavy-over-light plasma in an effective gravitational field with an embedded current sheet. This paper studies the linear stability of a slab current sheet with respect to reconnecting modes in the presence of a density gradient under the effect of a constant gravitational acceleration. We show that the presence of stratification and gravity modify the properties of the tearing mode instability both in the case of favorable and unfavorable stratification. Favorable stratification suppresses reconnection while unfavorable stratification strongly destabilizes the tearing mode. Furthermore, we show that the classical constant-{\psi} regime effectively does not exist, even for weak unfavorable stratification, for S>>1. Instead, the gravity-modified tearing progressively transitions into the G-mode, which is a gravity-driven reconnecting mode with a growth rate scaling as S^-1/3. As a consequence, unfavorable stratification only permits rapidly reconnecting modes.

physics.plasm-ph↗
arXiv2025

Investigation of Tearing Mode Stability Near Ideal Stability Boundaries Via Asymptotic Matching Techniques

A number of improvements to the TJ toroidal tearing mode code [Phys. Plasmas 31, 102507 (2024)] are documented. The TJ code is also successfully benchmarked against the STRIDE toroidal tearing mode code [Phys. Plasmas 25, 082502 (2018)]. Finally, the new capabilities of the TJ code are used to investigate the stability of tearing modes in tokamak plasmas as an ideal stability boundary, associated with either an external-kink or an internal-kink mode, is approached. All elements of the tearing stability matrix are found to tend to infinity as an ideal stability boundary is approached. Furthermore, as the stability boundary is approached, the eigenfunctions of the various tearing modes in the plasma, which are decoupled by sheared plasma rotation, are all found to morph into that of the marginally-stable ideal mode. However, the growth-rates and real frequencies of the various ``ideal-tearing-modes'' are different from one another. Moreover, the growth-rate of the ideal-tearing-mode that reconnects magnetic flux at the rational surface that lies closest to the edge of the plasma is the one that tends to a very large value as the stability boundary is approached. A relatively simple test for ideal stability that is capable of detecting stability boundaries for external-kink and internal-kink modes, even in the presence of a very close-fitting ideal wall, is described and verified.

physics.plasm-ph↗
arXiv2019

Analytic Theory of Edge Localized Mode Suppression by Static Resonant Magnetic Perturbations in H-mode Tokamak Discharges

An analytic theory of edge localized mode (ELM) suppression in an H-mode tokamak plasma via the application of a static, externally generated, resonant magnetic perturbation (RMP) is presented. This theory is based on the plausible hypothesis that mode penetration at the top of the pedestal is a necessary and sufficient condition for the RMP-induced suppression of ELMs. The theory also makes use of a number of key insights gained in a recent publication (Fitzpatrick R 2019). The first insight is that the response of the plasma to a particular helical component of the RMP, in the immediate vicinity of the associated resonant surface, is governed by nonlinear magnetic island physics, rather than by linear layer physics. The second insight is that neoclassical effects play a vital role in the physics of RMP-induced ELM suppression. The final insight is that plasma impurities play an important role in the physics of RMP-induced ELM suppression. The theory presented in this paper is employed to gain a better understanding ELM suppression in DIII-D and ITER H-mode discharges. It is found that ELM suppression is only possible when q_95 takes values that lie in certain narrow windows. Moreover, the widths of these windows decrease with increasing plasma density. Assuming a core plasma rotation of 20 krad/s, the window width for a model ITER H-mode discharge is found to be similar to, but slightly smaller than, the window width in a typical DIII-D H-mode discharge.

physics.plasm-ph↗
arXiv2019

Theory of Edge Localized Mode Suppression by Static Resonant Magnetic Perturbations in the DIII-D Tokamak

The plasma response to an externally generated, static, n=2, resonant magnetic perturbation (RMP) in the pedestal region of DIII-D discharge #158115 is investigated. In this particular discharge, the resonant amplitudes of the RMP are modulated in a cycloidal manner at a frequency of 1 Hz. Adopting the plausible hypothesis that mode penetration at the top of the pedestal is a necessary and sufficient condition for the RMP-induced suppression of edge localized modes (ELMs), recent cylindrical, nonlinear, reduced-magnetohydrodynamical (MHD) simulations performed by Hu, Nazikian, et al., (2019) can account, in a quantitative fashion, for the density-pump out and RMP-induced ELM suppression threshold observed in DIII-D discharge #158115. The primary aim of this paper is to employ analytic theory to further simplify the model of Hu, Nazikian, et al., in such a manner that a complete simulation of RMP-induced ELM-suppression in a DIII-D H-mode discharge can be performed in a matter of minutes of real time. A secondary aim is to gain a more exact understanding of the physical mechanism that underlies RMP-induced ELM suppression in the DIII-D tokamak.

physics.plasm-ph↗
arXiv2018

Vacuum Solution for Solov'ev's Equilibrium Configuration in Tokamaks

In this work, we have revisited the Solov'ev analytical solution for a tokamak equilibrium. We point out that the vacuum solution in the Solov'ev formulation is inapplicable, since a distributed current density is assumed to fill the vacuum. The realistic vacuum should be current-free. To amend this vacuum solution problem, we use Green's function method to compute the plasma current contribution, together with a homogeneous solution to the Grad-Shafranov equation, to construct the full solution. Matching with the Solov'ev solution on the last closed flux surface is performed to determine the homogeneous solution. The total solution is then extended into the vacuum region to get a realistic vacuum solution. We find that the actual vacuum solution is different from the Solov'ev solution in the vacuum region, especially the X-point structure. The X-point obtained at the last closed flux surface is not like the letter "X", and the expanded angle in the vacuum is larger than corresponding angle in the plasma at the null point. The results are important for understanding the X-point and separatrix structure. At the end of the paper, we have extended the classic Solovev's configuration to an ITER-like configuration, and obtained the full solution.

physics.plasm-ph↗
arXiv2018

Two-Fluid Nonlinear Theory of Response of Tokamak Plasma to Resonant Magnetic Perturbation

A comprehensive two-fluid nonlinear theory of magnetic reconnection driven at a single, tearing-stable, rational surface embedded in an H-mode tokamak plasma is presented. The surface is assumed to be resonant with one of the dominant helical harmonics of an applied resonant magnetic perturbation (RMP). The theory described in this paper is highly relevant to the problem of understanding the physics of RMP-induced edge localized mode (ELM) suppression in tokamak plasmas.

physics.plasm-ph↗
arXiv2016

Effect of Nonlinear Energy Transport on Neoclassical Tearing Mode Stability in Tokamak Plasmas

An investigation is made into the effect of the reduction in anomalous perpendicular electron heat transport inside the separatrix of a magnetic island chain associated with a neoclassical tearing mode in a tokamak plasma, due to the flattening of the electron temperature profile in this region, on the overall stability of the mode. The onset of the neoclassical tearing mode is governed by the ratio of the divergences of the parallel and perpendicular electron heat fluxes in the vicinity of the island chain. By increasing the degree of transport reduction, the onset of the mode, as the divergence ratio is gradually increased, can be made more and more abrupt. Eventually, when the degree of transport reduction passes a certain critical value, the onset of the neoclassical tearing mode becomes discontinuous. In other words, when some critical value of the divergence ratio is reached, there is a sudden bifurcation to a branch of neoclassical tearing mode solutions. Moreover, once this bifurcation has been triggered, the divergence ratio must reduced by a substantial factor to trigger the inverse bifurcation.

physics.plasm-ph↗
arXiv2015

An Improved Neoclassical Drift-Magnetohydrodynamical Fluid Model of Helical Magnetic Island Equilibria in Tokamak Plasmas

The effect of the perturbed ion polarization current on the stability of neoclassical tearing modes is calculated using an improved, neoclassical, four-field, drift-MHD model. The calculation involves the self-consistent determination of the pressure and scalar electric potential profiles in the vicinity of the associated magnetic island chain, which allows the chain's propagation velocity to be fixed. Two regimes are considered. First, a regime in which neoclassical ion poloidal flow damping is not strong enough to enhance the magnitude of the polarization current (relative to that found in slab geometry). Second, a regime in which neoclassical ion poloidal flow damping is strong enough to significantly enhance the magnitude of the polarization current. In both regimes, two types of solution are considered. First, a freely rotating solution (i.e., an island chain that is not interacting with a static, resonant, magnetic perturbation). Second, a locked solution (i.e., an island chain that has been brought to rest in the laboratory frame via interaction with a static, resonant, magnetic perturbation). In all cases, the polarization current is found to be either always stabilizing, or stabilizing provided that eta_i = d ln T_i/d ln n_e does not exceed some threshold value. In certain ranges of eta_i, the polarization current is found to have have a stabilizing effect on a freely rotating island, but a destabilizing effect on a corresponding locked island.

physics.plasm-ph↗
arXiv2004

Two-fluid magnetic island dynamics in slab geometry: I - Isolated islands

A set of reduced, 2-D, two-fluid, drift-MHD equations is derived. Using these equations, a complete and fully self-consistent solution is obtained for an isolated magnetic island propagating through a slab plasma with uniform but different ion and electron fluid velocities. The ion and electron fluid flow profiles around the island are uniquely determined, and are everywhere continuous. Moreover, the island phase-velocity is uniquely specified by the condition that there be zero net electromagnetic force acting on the island. Finally, the ion polarization current correction to the Rutherford island width evolution equation is evaluated, and found to be stabilizing provided that the anomalous perpendicular ion viscosity significantly exceeds the anomalous perpendicular electron viscosity.

physics.plasm-ph↗
arXiv2004

Two-fluid magnetic island dynamics in slab geometry: II - Islands interacting with resistive walls or static external resonant magnetic perturbations

The dynamics of a propagating magnetic island interacting with a resistive wall or a static external magnetic perturbation is investigated using two-fluid, drift-MHD theory in slab geometry. In both cases, the island equation of motion is found to take exactly the same form as that predicted by single-fluid MHD theory. Three separate ion polarization terms are found in the Rutherford island width evolution equation. The first is the drift-MHD polarization term for an isolated island, and is completely unaffected by interaction with a wall or magnetic perturbation. Next, there is the polarization term due to interaction with a wall or magnetic perturbation which is predicted by single-fluid MHD theory. Finally, there is a hybrid of the other two polarization terms. The sign of this term depends on many factors. However, under normal conditions, it is stabilizing if the unperturbed island propagates in the ion diamagnetic direction (in the lab. frame), and destabilizing if it propagates in the electron diamagnetic direction.

physics.plasm-ph↗